Our approach to the Sandia Verification and Validation Challenge Problem is to use probability bounds analysis (PBA) based on probabilistic representation for aleatory uncertainties and interval representation for (most) epistemic uncertainties. The nondeterministic model predictions thus take the form of p-boxes, or bounding cumulative distribution functions (CDFs) that contain all possible families of CDFs that could exist within the uncertainty bounds. The scarcity of experimental data provides little support for treatment of all uncertain inputs as purely aleatory uncertainties and also precludes significant calibration of the models. We instead seek to estimate the model form uncertainty at conditions where the experimental data are available, then extrapolate this uncertainty to conditions where no data exist. The modified area validation metric (MAVM) is employed to estimate the model form uncertainty which is important because the model involves significant simplifications (both geometric and physical nature) of the true system. The results of verification and validation processes are treated as additional interval-based uncertainties applied to the nondeterministic model predictions based on which the failure prediction is made. Based on the method employed, we estimate the probability of failure to be as large as 0.0034, concluding that the tanks are unsafe.
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March 2016
Research-Article
Probability Bounds Analysis Applied to the Sandia Verification and Validation Challenge Problem
Aniruddha Choudhary,
Aniruddha Choudhary
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: aniruddhac@gmail.com
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: aniruddhac@gmail.com
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Ian T. Voyles,
Ian T. Voyles
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: itvoyles@vt.edu
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: itvoyles@vt.edu
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Christopher J. Roy,
Christopher J. Roy
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
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William L. Oberkampf,
William L. Oberkampf
Mem. ASME
W. L. Oberkampf Consulting,
5112 Hidden Springs Trail,
Georgetown, TX 78633
e-mail: wloconsulting@gmail.com
W. L. Oberkampf Consulting,
5112 Hidden Springs Trail,
Georgetown, TX 78633
e-mail: wloconsulting@gmail.com
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Mayuresh Patil
Mayuresh Patil
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: mpatil@vt.edu
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: mpatil@vt.edu
Search for other works by this author on:
Aniruddha Choudhary
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: aniruddhac@gmail.com
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: aniruddhac@gmail.com
Ian T. Voyles
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: itvoyles@vt.edu
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: itvoyles@vt.edu
Christopher J. Roy
Mem. ASME
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
William L. Oberkampf
Mem. ASME
W. L. Oberkampf Consulting,
5112 Hidden Springs Trail,
Georgetown, TX 78633
e-mail: wloconsulting@gmail.com
W. L. Oberkampf Consulting,
5112 Hidden Springs Trail,
Georgetown, TX 78633
e-mail: wloconsulting@gmail.com
Mayuresh Patil
Aerospace and Ocean Engineering Department,
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: mpatil@vt.edu
Virginia Tech,
460 Old Turner Street,
Blacksburg, VA 24061
e-mail: mpatil@vt.edu
1Corresponding author.
Manuscript received February 8, 2015; final manuscript received July 31, 2015; published online February 19, 2016. Guest Editor: Kenneth Hu.
J. Verif. Valid. Uncert. Mar 2016, 1(1): 011003 (13 pages)
Published Online: February 19, 2016
Article history
Received:
February 8, 2015
Revised:
July 31, 2015
Accepted:
August 7, 2015
Citation
Choudhary, A., Voyles, I. T., Roy, C. J., Oberkampf, W. L., and Patil, M. (February 19, 2016). "Probability Bounds Analysis Applied to the Sandia Verification and Validation Challenge Problem." ASME. J. Verif. Valid. Uncert. March 2016; 1(1): 011003. https://doi.org/10.1115/1.4031285
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